Manifolds.jl

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Implement `translate_diff` and `inv_diff` for all groups at once?

28

Here is a suggestion to decrease the amount of code, and improve the user interface of `Manifolds.jl`. --- I suggest the **basic method to be implemented to be the left...

olivierverdier

Wrong parameter for `GroupExponentialRetraction`

1

Currently, `GroupExponentialRetraction` depends on a type `ActionDirectionAndSide`, but, unless I am mistaken, it should only depend on `GroupActionSide`. Put differently, the `GroupExponentialRetraction{LeftBackwardAction}` and `GroupExponentialRetraction{RightForwardAction}` *make no sense*. Indeed: in the...

olivierverdier

`mean` runtime-dispatch and allocations on Lie Groups - SE(2/3)

8

We use `mean` in a few performance-critical places and I've noticed it was one of the bottlenecks. For example: ```julia julia> @time mean(SpecialEuclidean(2), [ArrayPartition(SA[-1.,0], SA[1 0; 0 1.]), ArrayPartition(SA[1.,0], SA[1...

Affie

Ref. https://math.stackexchange.com/a/2017583

mateuszbaran

Description: [Quotient geometry with simple geodesics for the manifold of fixed-rank positive-semidefinite matrices](https://sites.uclouvain.be/absil/2018-06/quotient_geometry_preprint_final.pdf)

mateuszbaran

Add docs about error accumulation

2

A recent Slack discussion has an excellent example of catastrophic error accumulation on a sphere: ```julia julia> using Manifolds, LinearAlgebra, Manopt, ManifoldDiff, ReverseDiff julia> N = 10 10 julia> Z...

mateuszbaran

Manopt/Matlab has a nice function to numerically check retractions https://github.com/NicolasBoumal/manopt/blob/master/manopt/tools/checkretraction.m which requires that the exponential map is implemented. I think it should even be possible to check two retractions –...

kellertuer

Here are some methods on Kendall's shape spaces that could be implemented but won't be a part of #550 : * [ ] injectivity radius: http://nonlinearstudies.com/index.php/nonlinear/article/view/2026 * [ ] parallel...

mateuszbaran

See https://arxiv.org/abs/2204.07830

mateuszbaran